{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots, Measures, LaTeXStrings, Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hub_err (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sq_err(x) = x^2\n",
    "abs_err(x) = abs(x)\n",
    "hub_err(x) = abs(x) < 1 ? x^2/2 : abs(x) - 1/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "  930.315,1235.4 932.882,1237.48 935.45,1239.54 938.017,1241.59 940.585,1243.63 943.153,1245.64 945.72,1247.64 948.288,1249.63 950.855,1251.59 953.423,1253.55 \n",
       "  955.991,1255.48 958.558,1257.4 961.126,1259.31 963.693,1261.19 966.261,1263.07 968.828,1264.92 971.396,1266.76 973.964,1268.59 976.531,1270.39 979.099,1272.18 \n",
       "  981.666,1273.96 984.234,1275.72 986.802,1277.46 989.369,1279.19 991.937,1280.9 994.504,1282.6 997.072,1284.27 999.639,1285.94 1002.21,1287.58 1004.77,1289.22 \n",
       "  1007.34,1290.83 1009.91,1292.43 1012.48,1294.01 1015.04,1295.58 1017.61,1297.13 1020.18,1298.66 1022.75,1300.18 1025.32,1301.68 1027.88,1303.17 1030.45,1304.64 \n",
       "  1033.02,1306.09 1035.59,1307.53 1038.15,1308.95 1040.72,1310.36 1043.29,1311.75 1045.86,1313.12 1048.42,1314.48 1050.99,1315.82 1053.56,1317.15 1056.13,1318.46 \n",
       "  1058.69,1319.75 1061.26,1321.03 1063.83,1322.29 1066.4,1323.53 1068.96,1324.76 1071.53,1325.98 1074.1,1327.17 1076.67,1328.35 1079.23,1329.52 1081.8,1330.67 \n",
       "  1084.37,1331.8 1086.94,1332.92 1089.5,1334.02 1092.07,1335.1 1094.64,1336.17 1097.21,1337.22 1099.78,1338.26 1102.34,1339.28 1104.91,1340.28 1107.48,1341.27 \n",
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       "  1135.72,1351.08 1138.29,1351.88 1140.86,1352.66 1143.42,1353.42 1145.99,1354.17 1148.56,1354.9 1151.13,1355.61 1153.69,1356.31 1156.26,1356.99 1158.83,1357.66 \n",
       "  1161.4,1358.31 1163.96,1358.95 1166.53,1359.56 1169.1,1360.17 1171.67,1360.75 1174.24,1361.32 1176.8,1361.88 1179.37,1362.42 1181.94,1362.94 1184.51,1363.44 \n",
       "  1187.07,1363.93 1189.64,1364.41 1192.21,1364.87 1194.78,1365.31 1197.34,1365.73 1199.91,1366.14 1202.48,1366.54 1205.05,1366.92 1207.61,1367.28 1210.18,1367.62 \n",
       "  1212.75,1367.95 1215.32,1368.26 1217.88,1368.56 1220.45,1368.84 1223.02,1369.11 1225.59,1369.36 1228.15,1369.59 1230.72,1369.81 1233.29,1370.01 1235.86,1370.19 \n",
       "  1238.42,1370.36 1240.99,1370.51 1243.56,1370.65 1246.13,1370.77 1248.7,1370.88 1251.26,1370.96 1253.83,1371.04 1256.4,1371.09 1258.97,1371.13 1261.53,1371.16 \n",
       "  1264.1,1371.17 1266.67,1371.16 1269.24,1371.13 1271.8,1371.09 1274.37,1371.04 1276.94,1370.96 1279.51,1370.88 1282.07,1370.77 1284.64,1370.65 1287.21,1370.51 \n",
       "  1289.78,1370.36 1292.34,1370.19 1294.91,1370.01 1297.48,1369.81 1300.05,1369.59 1302.61,1369.36 1305.18,1369.11 1307.75,1368.84 1310.32,1368.56 1312.88,1368.26 \n",
       "  1315.45,1367.95 1318.02,1367.62 1320.59,1367.28 1323.15,1366.92 1325.72,1366.54 1328.29,1366.14 1330.86,1365.73 1333.43,1365.31 1335.99,1364.87 1338.56,1364.41 \n",
       "  1341.13,1363.93 1343.7,1363.44 1346.26,1362.94 1348.83,1362.42 1351.4,1361.88 1353.97,1361.32 1356.53,1360.75 1359.1,1360.17 1361.67,1359.56 1364.24,1358.95 \n",
       "  1366.8,1358.31 1369.37,1357.66 1371.94,1356.99 1374.51,1356.31 1377.07,1355.61 1379.64,1354.9 1382.21,1354.17 1384.78,1353.42 1387.34,1352.66 1389.91,1351.88 \n",
       "  1392.48,1351.08 1395.05,1350.27 1397.61,1349.44 1400.18,1348.6 1402.75,1347.74 1405.32,1346.86 1407.89,1345.97 1410.45,1345.06 1413.02,1344.14 1415.59,1343.2 \n",
       "  1418.16,1342.24 1420.72,1341.27 1423.29,1340.28 1425.86,1339.28 1428.43,1338.26 1430.99,1337.22 1433.56,1336.17 1436.13,1335.1 1438.7,1334.02 1441.26,1332.92 \n",
       "  1443.83,1331.8 1446.4,1330.67 1448.97,1329.52 1451.53,1328.35 1454.1,1327.17 1456.67,1325.98 1459.24,1324.76 1461.8,1323.53 1464.37,1322.29 1466.94,1321.03 \n",
       "  1469.51,1319.75 1472.07,1318.46 1474.64,1317.15 1477.21,1315.82 1479.78,1314.48 1482.35,1313.12 1484.91,1311.75 1487.48,1310.36 1490.05,1308.95 1492.62,1307.53 \n",
       "  1495.18,1306.09 1497.75,1304.64 1500.32,1303.17 1502.89,1301.68 1505.45,1300.18 1508.02,1298.66 1510.59,1297.13 1513.16,1295.58 1515.72,1294.01 1518.29,1292.43 \n",
       "  1520.86,1290.83 1523.43,1289.22 1525.99,1287.58 1528.56,1285.94 1531.13,1284.27 1533.7,1282.6 1536.26,1280.9 1538.83,1279.19 1541.4,1277.46 1543.97,1275.72 \n",
       "  1546.53,1273.96 1549.1,1272.18 1551.67,1270.39 1554.24,1268.59 1556.81,1266.76 1559.37,1264.92 1561.94,1263.07 1564.51,1261.19 1567.08,1259.31 1569.64,1257.4 \n",
       "  1572.21,1255.48 1574.78,1253.55 1577.35,1251.59 1579.91,1249.63 1582.48,1247.64 1585.05,1245.64 1587.62,1243.63 1590.18,1241.59 1592.75,1239.54 1595.32,1237.48 \n",
       "  1597.89,1235.4 1600.45,1233.3 1603.02,1231.19 1605.59,1229.06 1608.16,1226.92 1610.72,1224.75 1613.29,1222.58 1615.86,1220.38 1618.43,1218.18 1620.99,1215.95 \n",
       "  1623.56,1213.71 1626.13,1211.45 1628.7,1209.18 1631.26,1206.89 1633.83,1204.58 1636.4,1202.26 1638.97,1199.92 1641.54,1197.57 1644.1,1195.2 1646.67,1192.81 \n",
       "  1649.24,1190.41 1651.81,1187.99 1654.37,1185.56 1656.94,1183.11 1659.51,1180.64 1662.08,1178.16 1664.64,1175.66 1667.21,1173.15 1669.78,1170.62 1672.35,1168.07 \n",
       "  1674.91,1165.51 1677.48,1162.93 1680.05,1160.33 1682.62,1157.72 1685.18,1155.1 1687.75,1152.45 1690.32,1149.79 1692.89,1147.12 1695.45,1144.43 1698.02,1141.72 \n",
       "  1700.59,1139 1703.16,1136.26 1705.72,1133.5 1708.29,1130.73 1710.86,1127.94 1713.43,1125.14 1716,1122.32 1718.56,1119.48 1721.13,1116.63 1723.7,1113.76 \n",
       "  1726.27,1110.88 1728.83,1107.98 1731.4,1105.06 1733.97,1102.13 1736.54,1099.18 1739.1,1096.22 1741.67,1093.24 1744.24,1090.24 1746.81,1087.23 1749.37,1084.2 \n",
       "  1751.94,1081.16 1754.51,1078.09 1757.08,1075.02 1759.64,1071.93 1762.21,1068.82 1764.78,1065.69 1767.35,1062.55 1769.91,1059.39 1772.48,1056.22 1775.05,1053.03 \n",
       "  1777.62,1049.83 1780.18,1046.6 1782.75,1043.37 1785.32,1040.11 1787.89,1036.84 1790.46,1033.56 1793.02,1030.26 1795.59,1026.94 1798.16,1023.6 1800.73,1020.25 \n",
       "  1803.29,1016.89 1805.86,1013.51 1808.43,1010.11 1811,1006.69 1813.56,1003.26 1816.13,999.816 1818.7,996.354 1821.27,992.876 1823.83,989.381 1826.4,985.87 \n",
       "  1828.97,982.344 1831.54,978.801 1834.1,975.242 1836.67,971.667 1839.24,968.076 1841.81,964.469 1844.37,960.846 1846.94,957.207 1849.51,953.552 1852.08,949.88 \n",
       "  1854.64,946.193 1857.21,942.489 1859.78,938.77 1862.35,935.034 1864.92,931.283 1867.48,927.515 1870.05,923.731 1872.62,919.931 1875.19,916.115 1877.75,912.283 \n",
       "  1880.32,908.435 1882.89,904.571 1885.46,900.691 1888.02,896.795 1890.59,892.883 1893.16,888.954 1895.73,885.01 1898.29,881.049 1900.86,877.073 1903.43,873.08 \n",
       "  1906,869.071 1908.56,865.046 1911.13,861.006 1913.7,856.949 1916.27,852.876 1918.83,848.787 1921.4,844.682 1923.97,840.56 1926.54,836.423 1929.1,832.27 \n",
       "  1931.67,828.1 1934.24,823.915 1936.81,819.713 1939.37,815.496 1941.94,811.262 1944.51,807.012 1947.08,802.747 1949.65,798.465 1952.21,794.167 1954.78,789.853 \n",
       "  1957.35,785.523 1959.92,781.177 1962.48,776.815 1965.05,772.436 1967.62,768.042 1970.19,763.632 1972.75,759.205 1975.32,754.763 1977.89,750.304 1980.46,745.829 \n",
       "  1983.02,741.339 1985.59,736.832 1988.16,732.309 1990.73,727.77 1993.29,723.215 1995.86,718.644 1998.43,714.057 2001,709.454 2003.56,704.834 2006.13,700.199 \n",
       "  2008.7,695.548 2011.27,690.88 2013.83,686.197 2016.4,681.497 2018.97,676.781 2021.54,672.05 2024.11,667.302 2026.67,662.538 2029.24,657.758 2031.81,652.962 \n",
       "  2034.38,648.15 2036.94,643.322 2039.51,638.478 2042.08,633.617 2044.65,628.741 2047.21,623.849 2049.78,618.94 2052.35,614.016 2054.92,609.075 2057.48,604.118 \n",
       "  2060.05,599.146 2062.62,594.157 2065.19,589.152 2067.75,584.131 2070.32,579.094 2072.89,574.041 2075.46,568.972 2078.02,563.887 2080.59,558.785 2083.16,553.668 \n",
       "  2085.73,548.535 2088.29,543.385 2090.86,538.22 2093.43,533.038 2096,527.84 2098.57,522.627 2101.13,517.397 2103.7,512.151 2106.27,506.889 2108.84,501.611 \n",
       "  2111.4,496.317 2113.97,491.007 2116.54,485.68 2119.11,480.338 2121.67,474.98 2124.24,469.605 2126.81,464.215 2129.38,458.808 2131.94,453.386 2134.51,447.947 \n",
       "  2137.08,442.492 2139.65,437.022 2142.21,431.535 2144.78,426.032 2147.35,420.513 2149.92,414.978 2152.48,409.426 2155.05,403.859 2157.62,398.276 2160.19,392.677 \n",
       "  2162.75,387.061 2165.32,381.43 2167.89,375.782 2170.46,370.119 2173.03,364.439 2175.59,358.743 2178.16,353.031 2180.73,347.303 2183.3,341.559 2185.86,335.799 \n",
       "  2188.43,330.023 2191,324.231 2193.57,318.423 2196.13,312.599 2198.7,306.758 2201.27,300.902 2203.84,295.029 2206.4,289.141 2208.97,283.236 2211.54,277.316 \n",
       "  2214.11,271.379 2216.67,265.426 2219.24,259.457 2221.81,253.472 2224.38,247.471 2226.94,241.454 2229.51,235.421 2232.08,229.372 2234.65,223.306 2237.21,217.225 \n",
       "  2239.78,211.128 2242.35,205.014 2244.92,198.884 2247.48,192.739 2250.05,186.577 2252.62,180.399 2255.19,174.206 2257.76,167.996 2260.32,161.77 2262.89,155.528 \n",
       "  2265.46,149.27 2268.03,142.995 2270.59,136.705 2273.16,130.399 2275.73,124.076 2278.3,117.738 2280.86,111.384 2283.43,105.013 2286,98.6264 2288.57,92.2237 \n",
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       "  1007.34,1210.5 1009.91,1212.1 1012.48,1213.71 1015.04,1215.32 1017.61,1216.92 1020.18,1218.53 1022.75,1220.14 1025.32,1221.74 1027.88,1223.35 1030.45,1224.96 \n",
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       "  1058.69,1242.63 1061.26,1244.24 1063.83,1245.84 1066.4,1247.45 1068.96,1249.06 1071.53,1250.66 1074.1,1252.27 1076.67,1253.88 1079.23,1255.48 1081.8,1257.09 \n",
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       "  1161.4,1306.9 1163.96,1308.5 1166.53,1310.11 1169.1,1311.72 1171.67,1313.32 1174.24,1314.93 1176.8,1316.54 1179.37,1318.14 1181.94,1319.75 1184.51,1321.36 \n",
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       "  1212.75,1339.03 1215.32,1340.64 1217.88,1342.24 1220.45,1343.85 1223.02,1345.46 1225.59,1347.06 1228.15,1348.67 1230.72,1350.28 1233.29,1351.88 1235.86,1353.49 \n",
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       "  1264.1,1371.17 1266.67,1369.56 1269.24,1367.95 1271.8,1366.34 1274.37,1364.74 1276.94,1363.13 1279.51,1361.52 1282.07,1359.92 1284.64,1358.31 1287.21,1356.7 \n",
       "  1289.78,1355.1 1292.34,1353.49 1294.91,1351.88 1297.48,1350.28 1300.05,1348.67 1302.61,1347.06 1305.18,1345.46 1307.75,1343.85 1310.32,1342.24 1312.88,1340.64 \n",
       "  1315.45,1339.03 1318.02,1337.42 1320.59,1335.82 1323.15,1334.21 1325.72,1332.6 1328.29,1331 1330.86,1329.39 1333.43,1327.78 1335.99,1326.18 1338.56,1324.57 \n",
       "  1341.13,1322.96 1343.7,1321.36 1346.26,1319.75 1348.83,1318.14 1351.4,1316.54 1353.97,1314.93 1356.53,1313.32 1359.1,1311.72 1361.67,1310.11 1364.24,1308.5 \n",
       "  1366.8,1306.9 1369.37,1305.29 1371.94,1303.68 1374.51,1302.08 1377.07,1300.47 1379.64,1298.86 1382.21,1297.26 1384.78,1295.65 1387.34,1294.04 1389.91,1292.44 \n",
       "  1392.48,1290.83 1395.05,1289.22 1397.61,1287.62 1400.18,1286.01 1402.75,1284.4 1405.32,1282.8 1407.89,1281.19 1410.45,1279.58 1413.02,1277.98 1415.59,1276.37 \n",
       "  1418.16,1274.76 1420.72,1273.16 1423.29,1271.55 1425.86,1269.94 1428.43,1268.34 1430.99,1266.73 1433.56,1265.12 1436.13,1263.52 1438.7,1261.91 1441.26,1260.3 \n",
       "  1443.83,1258.7 1446.4,1257.09 1448.97,1255.48 1451.53,1253.88 1454.1,1252.27 1456.67,1250.66 1459.24,1249.06 1461.8,1247.45 1464.37,1245.84 1466.94,1244.24 \n",
       "  1469.51,1242.63 1472.07,1241.02 1474.64,1239.42 1477.21,1237.81 1479.78,1236.2 1482.35,1234.6 1484.91,1232.99 1487.48,1231.38 1490.05,1229.78 1492.62,1228.17 \n",
       "  1495.18,1226.56 1497.75,1224.96 1500.32,1223.35 1502.89,1221.74 1505.45,1220.14 1508.02,1218.53 1510.59,1216.92 1513.16,1215.32 1515.72,1213.71 1518.29,1212.1 \n",
       "  1520.86,1210.5 1523.43,1208.89 1525.99,1207.28 1528.56,1205.67 1531.13,1204.07 1533.7,1202.46 1536.26,1200.85 1538.83,1199.25 1541.4,1197.64 1543.97,1196.03 \n",
       "  1546.53,1194.43 1549.1,1192.82 1551.67,1191.21 1554.24,1189.61 1556.81,1188 1559.37,1186.39 1561.94,1184.79 1564.51,1183.18 1567.08,1181.57 1569.64,1179.97 \n",
       "  1572.21,1178.36 1574.78,1176.75 1577.35,1175.15 1579.91,1173.54 1582.48,1171.93 1585.05,1170.33 1587.62,1168.72 1590.18,1167.11 1592.75,1165.51 1595.32,1163.9 \n",
       "  1597.89,1162.29 1600.45,1160.69 1603.02,1159.08 1605.59,1157.47 1608.16,1155.87 1610.72,1154.26 1613.29,1152.65 1615.86,1151.05 1618.43,1149.44 1620.99,1147.83 \n",
       "  1623.56,1146.23 1626.13,1144.62 1628.7,1143.01 1631.26,1141.41 1633.83,1139.8 1636.4,1138.19 1638.97,1136.59 1641.54,1134.98 1644.1,1133.37 1646.67,1131.77 \n",
       "  1649.24,1130.16 1651.81,1128.55 1654.37,1126.95 1656.94,1125.34 1659.51,1123.73 1662.08,1122.13 1664.64,1120.52 1667.21,1118.91 1669.78,1117.31 1672.35,1115.7 \n",
       "  1674.91,1114.09 1677.48,1112.49 1680.05,1110.88 1682.62,1109.27 1685.18,1107.67 1687.75,1106.06 1690.32,1104.45 1692.89,1102.85 1695.45,1101.24 1698.02,1099.63 \n",
       "  1700.59,1098.03 1703.16,1096.42 1705.72,1094.81 1708.29,1093.21 1710.86,1091.6 1713.43,1089.99 1716,1088.39 1718.56,1086.78 1721.13,1085.17 1723.7,1083.57 \n",
       "  1726.27,1081.96 1728.83,1080.35 1731.4,1078.75 1733.97,1077.14 1736.54,1075.53 1739.1,1073.93 1741.67,1072.32 1744.24,1070.71 1746.81,1069.11 1749.37,1067.5 \n",
       "  1751.94,1065.89 1754.51,1064.29 1757.08,1062.68 1759.64,1061.07 1762.21,1059.47 1764.78,1057.86 1767.35,1056.25 1769.91,1054.65 1772.48,1053.04 1775.05,1051.43 \n",
       "  1777.62,1049.83 1780.18,1048.22 1782.75,1046.61 1785.32,1045 1787.89,1043.4 1790.46,1041.79 1793.02,1040.18 1795.59,1038.58 1798.16,1036.97 1800.73,1035.36 \n",
       "  1803.29,1033.76 1805.86,1032.15 1808.43,1030.54 1811,1028.94 1813.56,1027.33 1816.13,1025.72 1818.7,1024.12 1821.27,1022.51 1823.83,1020.9 1826.4,1019.3 \n",
       "  1828.97,1017.69 1831.54,1016.08 1834.1,1014.48 1836.67,1012.87 1839.24,1011.26 1841.81,1009.66 1844.37,1008.05 1846.94,1006.44 1849.51,1004.84 1852.08,1003.23 \n",
       "  1854.64,1001.62 1857.21,1000.02 1859.78,998.411 1862.35,996.804 1864.92,995.197 1867.48,993.591 1870.05,991.984 1872.62,990.377 1875.19,988.77 1877.75,987.164 \n",
       "  1880.32,985.557 1882.89,983.95 1885.46,982.344 1888.02,980.737 1890.59,979.13 1893.16,977.524 1895.73,975.917 1898.29,974.31 1900.86,972.703 1903.43,971.097 \n",
       "  1906,969.49 1908.56,967.883 1911.13,966.277 1913.7,964.67 1916.27,963.063 1918.83,961.457 1921.4,959.85 1923.97,958.243 1926.54,956.636 1929.1,955.03 \n",
       "  1931.67,953.423 1934.24,951.816 1936.81,950.21 1939.37,948.603 1941.94,946.996 1944.51,945.39 1947.08,943.783 1949.65,942.176 1952.21,940.569 1954.78,938.963 \n",
       "  1957.35,937.356 1959.92,935.749 1962.48,934.143 1965.05,932.536 1967.62,930.929 1970.19,929.323 1972.75,927.716 1975.32,926.109 1977.89,924.502 1980.46,922.896 \n",
       "  1983.02,921.289 1985.59,919.682 1988.16,918.076 1990.73,916.469 1993.29,914.862 1995.86,913.256 1998.43,911.649 2001,910.042 2003.56,908.435 2006.13,906.829 \n",
       "  2008.7,905.222 2011.27,903.615 2013.83,902.009 2016.4,900.402 2018.97,898.795 2021.54,897.189 2024.11,895.582 2026.67,893.975 2029.24,892.368 2031.81,890.762 \n",
       "  2034.38,889.155 2036.94,887.548 2039.51,885.942 2042.08,884.335 2044.65,882.728 2047.21,881.122 2049.78,879.515 2052.35,877.908 2054.92,876.301 2057.48,874.695 \n",
       "  2060.05,873.088 2062.62,871.481 2065.19,869.875 2067.75,868.268 2070.32,866.661 2072.89,865.055 2075.46,863.448 2078.02,861.841 2080.59,860.234 2083.16,858.628 \n",
       "  2085.73,857.021 2088.29,855.414 2090.86,853.808 2093.43,852.201 2096,850.594 2098.57,848.988 2101.13,847.381 2103.7,845.774 2106.27,844.167 2108.84,842.561 \n",
       "  2111.4,840.954 2113.97,839.347 2116.54,837.741 2119.11,836.134 2121.67,834.527 2124.24,832.921 2126.81,831.314 2129.38,829.707 2131.94,828.1 2134.51,826.494 \n",
       "  2137.08,824.887 2139.65,823.28 2142.21,821.674 2144.78,820.067 2147.35,818.46 2149.92,816.854 2152.48,815.247 2155.05,813.64 2157.62,812.033 2160.19,810.427 \n",
       "  2162.75,808.82 2165.32,807.213 2167.89,805.607 2170.46,804 2173.03,802.393 2175.59,800.786 2178.16,799.18 2180.73,797.573 2183.3,795.966 2185.86,794.36 \n",
       "  2188.43,792.753 2191,791.146 2193.57,789.54 2196.13,787.933 2198.7,786.326 2201.27,784.719 2203.84,783.113 2206.4,781.506 2208.97,779.899 2211.54,778.293 \n",
       "  2214.11,776.686 2216.67,775.079 2219.24,773.473 2221.81,771.866 2224.38,770.259 2226.94,768.652 2229.51,767.046 2232.08,765.439 2234.65,763.832 2237.21,762.226 \n",
       "  2239.78,760.619 2242.35,759.012 2244.92,757.406 2247.48,755.799 2250.05,754.192 2252.62,752.585 2255.19,750.979 2257.76,749.372 2260.32,747.765 2262.89,746.159 \n",
       "  2265.46,744.552 2268.03,742.945 2270.59,741.339 2273.16,739.732 2275.73,738.125 2278.3,736.518 2280.86,734.912 2283.43,733.305 2286,731.698 2288.57,730.092 \n",
       "  2291.13,728.485 \n",
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       "  262.743,905.222 265.311,906.829 267.878,908.435 270.446,910.042 273.013,911.649 275.581,913.256 278.149,914.862 280.716,916.469 283.284,918.076 285.851,919.682 \n",
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       "  1110.05,1356.7 1112.61,1357.18 1115.18,1357.65 1117.75,1358.11 1120.32,1358.57 1122.88,1359.01 1125.45,1359.45 1128.02,1359.88 1130.59,1360.3 1133.15,1360.72 \n",
       "  1135.72,1361.12 1138.29,1361.52 1140.86,1361.91 1143.42,1362.29 1145.99,1362.67 1148.56,1363.03 1151.13,1363.39 1153.69,1363.74 1156.26,1364.08 1158.83,1364.41 \n",
       "  1161.4,1364.74 1163.96,1365.06 1166.53,1365.36 1169.1,1365.67 1171.67,1365.96 1174.24,1366.24 1176.8,1366.52 1179.37,1366.79 1181.94,1367.05 1184.51,1367.3 \n",
       "  1187.07,1367.55 1189.64,1367.79 1192.21,1368.02 1194.78,1368.24 1197.34,1368.45 1199.91,1368.65 1202.48,1368.85 1205.05,1369.04 1207.61,1369.22 1210.18,1369.39 \n",
       "  1212.75,1369.56 1215.32,1369.72 1217.88,1369.86 1220.45,1370 1223.02,1370.14 1225.59,1370.26 1228.15,1370.38 1230.72,1370.49 1233.29,1370.59 1235.86,1370.68 \n",
       "  1238.42,1370.76 1240.99,1370.84 1243.56,1370.91 1246.13,1370.97 1248.7,1371.02 1251.26,1371.06 1253.83,1371.1 1256.4,1371.13 1258.97,1371.15 1261.53,1371.16 \n",
       "  1264.1,1371.17 1266.67,1371.16 1269.24,1371.15 1271.8,1371.13 1274.37,1371.1 1276.94,1371.06 1279.51,1371.02 1282.07,1370.97 1284.64,1370.91 1287.21,1370.84 \n",
       "  1289.78,1370.76 1292.34,1370.68 1294.91,1370.59 1297.48,1370.49 1300.05,1370.38 1302.61,1370.26 1305.18,1370.14 1307.75,1370 1310.32,1369.86 1312.88,1369.72 \n",
       "  1315.45,1369.56 1318.02,1369.39 1320.59,1369.22 1323.15,1369.04 1325.72,1368.85 1328.29,1368.65 1330.86,1368.45 1333.43,1368.24 1335.99,1368.02 1338.56,1367.79 \n",
       "  1341.13,1367.55 1343.7,1367.3 1346.26,1367.05 1348.83,1366.79 1351.4,1366.52 1353.97,1366.24 1356.53,1365.96 1359.1,1365.67 1361.67,1365.36 1364.24,1365.06 \n",
       "  1366.8,1364.74 1369.37,1364.41 1371.94,1364.08 1374.51,1363.74 1377.07,1363.39 1379.64,1363.03 1382.21,1362.67 1384.78,1362.29 1387.34,1361.91 1389.91,1361.52 \n",
       "  1392.48,1361.12 1395.05,1360.72 1397.61,1360.3 1400.18,1359.88 1402.75,1359.45 1405.32,1359.01 1407.89,1358.57 1410.45,1358.11 1413.02,1357.65 1415.59,1357.18 \n",
       "  1418.16,1356.7 1420.72,1356.22 1423.29,1355.72 1425.86,1355.22 1428.43,1354.71 1430.99,1354.19 1433.56,1353.67 1436.13,1353.13 1438.7,1352.59 1441.26,1352.04 \n",
       "  1443.83,1351.48 1446.4,1350.92 1448.97,1350.34 1451.53,1349.76 1454.1,1349.17 1456.67,1348.57 1459.24,1347.96 1461.8,1347.35 1464.37,1346.73 1466.94,1346.1 \n",
       "  1469.51,1345.46 1472.07,1344.81 1474.64,1344.16 1477.21,1343.49 1479.78,1342.82 1482.35,1342.14 1484.91,1341.46 1487.48,1340.76 1490.05,1340.06 1492.62,1339.35 \n",
       "  1495.18,1338.63 1497.75,1337.9 1500.32,1337.17 1502.89,1336.42 1505.45,1335.67 1508.02,1334.91 1510.59,1334.15 1513.16,1333.37 1515.72,1332.59 1518.29,1331.8 \n",
       "  1520.86,1331 1523.43,1330.19 1525.99,1329.37 1528.56,1328.55 1531.13,1327.72 1533.7,1326.88 1536.26,1326.03 1538.83,1325.18 1541.4,1324.31 1543.97,1323.44 \n",
       "  1546.53,1322.56 1549.1,1321.67 1551.67,1320.78 1554.24,1319.88 1556.81,1318.96 1559.37,1318.04 1561.94,1317.12 1564.51,1316.18 1567.08,1315.24 1569.64,1314.28 \n",
       "  1572.21,1313.32 1574.78,1312.36 1577.35,1311.38 1579.91,1310.4 1582.48,1309.4 1585.05,1308.4 1587.62,1307.4 1590.18,1306.38 1592.75,1305.35 1595.32,1304.32 \n",
       "  1597.89,1303.28 1600.45,1302.23 1603.02,1301.18 1605.59,1300.11 1608.16,1299.04 1610.72,1297.96 1613.29,1296.87 1615.86,1295.77 1618.43,1294.67 1620.99,1293.56 \n",
       "  1623.56,1292.44 1626.13,1291.31 1628.7,1290.17 1631.26,1289.03 1633.83,1287.87 1636.4,1286.71 1638.97,1285.54 1641.54,1284.37 1644.1,1283.18 1646.67,1281.99 \n",
       "  1649.24,1280.79 1651.81,1279.58 1654.37,1278.36 1656.94,1277.14 1659.51,1275.9 1662.08,1274.66 1664.64,1273.41 1667.21,1272.16 1669.78,1270.89 1672.35,1269.62 \n",
       "  1674.91,1268.34 1677.48,1267.05 1680.05,1265.75 1682.62,1264.44 1685.18,1263.13 1687.75,1261.81 1690.32,1260.48 1692.89,1259.14 1695.45,1257.8 1698.02,1256.44 \n",
       "  1700.59,1255.08 1703.16,1253.71 1705.72,1252.33 1708.29,1250.95 1710.86,1249.55 1713.43,1248.15 1716,1246.74 1718.56,1245.32 1721.13,1243.9 1723.7,1242.46 \n",
       "  1726.27,1241.02 1728.83,1239.57 1731.4,1238.11 1733.97,1236.65 1736.54,1235.17 1739.1,1233.69 1741.67,1232.2 1744.24,1230.7 1746.81,1229.2 1749.37,1227.68 \n",
       "  1751.94,1226.16 1754.51,1224.63 1757.08,1223.09 1759.64,1221.55 1762.21,1219.99 1764.78,1218.43 1767.35,1216.86 1769.91,1215.28 1772.48,1213.69 1775.05,1212.1 \n",
       "  1777.62,1210.5 1780.18,1208.89 1782.75,1207.28 1785.32,1205.67 1787.89,1204.07 1790.46,1202.46 1793.02,1200.85 1795.59,1199.25 1798.16,1197.64 1800.73,1196.03 \n",
       "  1803.29,1194.43 1805.86,1192.82 1808.43,1191.21 1811,1189.61 1813.56,1188 1816.13,1186.39 1818.7,1184.79 1821.27,1183.18 1823.83,1181.57 1826.4,1179.97 \n",
       "  1828.97,1178.36 1831.54,1176.75 1834.1,1175.15 1836.67,1173.54 1839.24,1171.93 1841.81,1170.33 1844.37,1168.72 1846.94,1167.11 1849.51,1165.51 1852.08,1163.9 \n",
       "  1854.64,1162.29 1857.21,1160.69 1859.78,1159.08 1862.35,1157.47 1864.92,1155.87 1867.48,1154.26 1870.05,1152.65 1872.62,1151.05 1875.19,1149.44 1877.75,1147.83 \n",
       "  1880.32,1146.23 1882.89,1144.62 1885.46,1143.01 1888.02,1141.41 1890.59,1139.8 1893.16,1138.19 1895.73,1136.59 1898.29,1134.98 1900.86,1133.37 1903.43,1131.77 \n",
       "  1906,1130.16 1908.56,1128.55 1911.13,1126.95 1913.7,1125.34 1916.27,1123.73 1918.83,1122.13 1921.4,1120.52 1923.97,1118.91 1926.54,1117.31 1929.1,1115.7 \n",
       "  1931.67,1114.09 1934.24,1112.49 1936.81,1110.88 1939.37,1109.27 1941.94,1107.67 1944.51,1106.06 1947.08,1104.45 1949.65,1102.85 1952.21,1101.24 1954.78,1099.63 \n",
       "  1957.35,1098.03 1959.92,1096.42 1962.48,1094.81 1965.05,1093.21 1967.62,1091.6 1970.19,1089.99 1972.75,1088.39 1975.32,1086.78 1977.89,1085.17 1980.46,1083.57 \n",
       "  1983.02,1081.96 1985.59,1080.35 1988.16,1078.75 1990.73,1077.14 1993.29,1075.53 1995.86,1073.93 1998.43,1072.32 2001,1070.71 2003.56,1069.11 2006.13,1067.5 \n",
       "  2008.7,1065.89 2011.27,1064.29 2013.83,1062.68 2016.4,1061.07 2018.97,1059.47 2021.54,1057.86 2024.11,1056.25 2026.67,1054.65 2029.24,1053.04 2031.81,1051.43 \n",
       "  2034.38,1049.83 2036.94,1048.22 2039.51,1046.61 2042.08,1045 2044.65,1043.4 2047.21,1041.79 2049.78,1040.18 2052.35,1038.58 2054.92,1036.97 2057.48,1035.36 \n",
       "  2060.05,1033.76 2062.62,1032.15 2065.19,1030.54 2067.75,1028.94 2070.32,1027.33 2072.89,1025.72 2075.46,1024.12 2078.02,1022.51 2080.59,1020.9 2083.16,1019.3 \n",
       "  2085.73,1017.69 2088.29,1016.08 2090.86,1014.48 2093.43,1012.87 2096,1011.26 2098.57,1009.66 2101.13,1008.05 2103.7,1006.44 2106.27,1004.84 2108.84,1003.23 \n",
       "  2111.4,1001.62 2113.97,1000.02 2116.54,998.411 2119.11,996.804 2121.67,995.197 2124.24,993.591 2126.81,991.984 2129.38,990.377 2131.94,988.77 2134.51,987.164 \n",
       "  2137.08,985.557 2139.65,983.95 2142.21,982.344 2144.78,980.737 2147.35,979.13 2149.92,977.524 2152.48,975.917 2155.05,974.31 2157.62,972.703 2160.19,971.097 \n",
       "  2162.75,969.49 2165.32,967.883 2167.89,966.277 2170.46,964.67 2173.03,963.063 2175.59,961.457 2178.16,959.85 2180.73,958.243 2183.3,956.636 2185.86,955.03 \n",
       "  2188.43,953.423 2191,951.816 2193.57,950.21 2196.13,948.603 2198.7,946.996 2201.27,945.39 2203.84,943.783 2206.4,942.176 2208.97,940.569 2211.54,938.963 \n",
       "  2214.11,937.356 2216.67,935.749 2219.24,934.143 2221.81,932.536 2224.38,930.929 2226.94,929.323 2229.51,927.716 2232.08,926.109 2234.65,924.502 2237.21,922.896 \n",
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     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_grid=-2:0.005:2\n",
    "\n",
    "p1 = plot(x_grid,sq_err.(x_grid),label = \"Squared loss\", \n",
    "    legend=:topleft, xlabel = L\"\\hat{y}^{(i)} - y^{(i)}\", ylabel=\"Loss\",lw=2,legendfont=font(12))\n",
    "plot!(x_grid,abs_err.(x_grid),label = \"Absolute loss\",lw=2)\n",
    "plot!(x_grid,hub_err.(x_grid),label = \"Huber loss (δ=1)\",lw=2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "savefig(\"~/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_2_figures/errs_funs.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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       "  909.031,1068.47 911.546,1063.3 914.061,1058.09 916.577,1052.83 919.092,1047.54 921.607,1042.2 924.122,1036.83 926.637,1031.41 929.153,1025.95 931.668,1020.46 \n",
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       "  984.487,897.143 987.002,890.959 989.517,884.753 992.033,878.526 994.548,872.28 997.063,866.014 999.578,859.732 1002.09,853.432 1004.61,847.118 1007.12,840.789 \n",
       "  1009.64,834.446 1012.15,828.092 1014.67,821.727 1017.18,815.351 1019.7,808.968 1022.22,802.576 1024.73,796.179 1027.25,789.776 1029.76,783.37 1032.28,776.961 \n",
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       "  1059.94,706.666 1062.46,700.329 1064.97,694.006 1067.49,687.7 1070,681.411 1072.52,675.141 1075.03,668.892 1077.55,662.664 1080.06,656.46 1082.58,650.281 \n",
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       "  1160.55,478.885 1163.07,474.257 1165.58,469.699 1168.1,465.215 1170.61,460.804 1173.13,456.468 1175.64,452.208 1178.16,448.026 1180.67,443.922 1183.19,439.898 \n",
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       "  1210.86,401.203 1213.37,398.218 1215.89,395.326 1218.4,392.527 1220.92,389.823 1223.43,387.214 1225.95,384.701 1228.46,382.285 1230.98,379.967 1233.49,377.746 \n",
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       "  1261.16,359.968 1263.67,358.969 1266.19,358.074 1268.7,357.283 1271.22,356.598 1273.74,356.017 1276.25,355.542 1278.77,355.173 1281.28,354.908 1283.8,354.75 \n",
       "  1286.31,354.697 1288.83,354.75 1291.34,354.908 1293.86,355.173 1296.37,355.542 1298.89,356.017 1301.4,356.598 1303.92,357.283 1306.43,358.074 1308.95,358.969 \n",
       "  1311.46,359.968 1313.98,361.072 1316.49,362.279 1319.01,363.59 1321.52,365.004 1324.04,366.52 1326.55,368.139 1329.07,369.859 1331.58,371.681 1334.1,373.603 \n",
       "  1336.62,375.625 1339.13,377.746 1341.65,379.967 1344.16,382.285 1346.68,384.701 1349.19,387.214 1351.71,389.823 1354.22,392.527 1356.74,395.326 1359.25,398.218 \n",
       "  1361.77,401.203 1364.28,404.28 1366.8,407.448 1369.31,410.706 1371.83,414.053 1374.34,417.489 1376.86,421.012 1379.37,424.621 1381.89,428.315 1384.4,432.093 \n",
       "  1386.92,435.955 1389.43,439.898 1391.95,443.922 1394.46,448.026 1396.98,452.208 1399.5,456.468 1402.01,460.804 1404.53,465.215 1407.04,469.699 1409.56,474.257 \n",
       "  1412.07,478.885 1414.59,483.583 1417.1,488.35 1419.62,493.184 1422.13,498.085 1424.65,503.05 1427.16,508.078 1429.68,513.169 1432.19,518.32 1434.71,523.53 \n",
       "  1437.22,528.798 1439.74,534.123 1442.25,539.503 1444.77,544.936 1447.28,550.422 1449.8,555.959 1452.31,561.545 1454.83,567.179 1457.34,572.86 1459.86,578.585 \n",
       "  1462.38,584.354 1464.89,590.166 1467.41,596.018 1469.92,601.91 1472.44,607.839 1474.95,613.805 1477.47,619.805 1479.98,625.839 1482.5,631.905 1485.01,638.002 \n",
       "  1487.53,644.127 1490.04,650.281 1492.56,656.46 1495.07,662.664 1497.59,668.892 1500.1,675.141 1502.62,681.411 1505.13,687.7 1507.65,694.006 1510.16,700.329 \n",
       "  1512.68,706.666 1515.19,713.017 1517.71,719.379 1520.22,725.753 1522.74,732.136 1525.26,738.526 1527.77,744.923 1530.29,751.326 1532.8,757.732 1535.32,764.141 \n",
       "  1537.83,770.551 1540.35,776.961 1542.86,783.37 1545.38,789.776 1547.89,796.179 1550.41,802.576 1552.92,808.968 1555.44,815.351 1557.95,821.727 1560.47,828.092 \n",
       "  1562.98,834.446 1565.5,840.789 1568.01,847.118 1570.53,853.432 1573.04,859.732 1575.56,866.014 1578.07,872.28 1580.59,878.526 1583.1,884.753 1585.62,890.959 \n",
       "  1588.14,897.143 1590.65,903.305 1593.17,909.444 1595.68,915.557 1598.2,921.646 1600.71,927.708 1603.23,933.742 1605.74,939.749 1608.26,945.727 1610.77,951.675 \n",
       "  1613.29,957.592 1615.8,963.478 1618.32,969.332 1620.83,975.154 1623.35,980.941 1625.86,986.695 1628.38,992.413 1630.89,998.096 1633.41,1003.74 1635.92,1009.35 \n",
       "  1638.44,1014.92 1640.95,1020.46 1643.47,1025.95 1645.98,1031.41 1648.5,1036.83 1651.02,1042.2 1653.53,1047.54 1656.05,1052.83 1658.56,1058.09 1661.08,1063.3 \n",
       "  1663.59,1068.47 1666.11,1073.59 1668.62,1078.67 1671.14,1083.71 1673.65,1088.71 1676.17,1093.66 1678.68,1098.56 1681.2,1103.42 1683.71,1108.24 1686.23,1113.01 \n",
       "  1688.74,1117.73 1691.26,1122.41 1693.77,1127.04 1696.29,1131.63 1698.8,1136.17 1701.32,1140.66 1703.83,1145.11 1706.35,1149.51 1708.86,1153.86 1711.38,1158.17 \n",
       "  1713.9,1162.43 1716.41,1166.64 1718.93,1170.81 1721.44,1174.92 1723.96,1178.99 1726.47,1183.02 1728.99,1186.99 1731.5,1190.92 1734.02,1194.81 1736.53,1198.64 \n",
       "  1739.05,1202.43 1741.56,1206.17 1744.08,1209.87 1746.59,1213.51 1749.11,1217.12 1751.62,1220.67 1754.14,1224.18 1756.65,1227.64 1759.17,1231.06 1761.68,1234.43 \n",
       "  1764.2,1237.76 1766.71,1241.04 1769.23,1244.27 1771.74,1247.46 1774.26,1250.61 1776.78,1253.71 1779.29,1256.76 1781.81,1259.78 1784.32,1262.74 1786.84,1265.67 \n",
       "  1789.35,1268.55 1791.87,1271.39 1794.38,1274.19 1796.9,1276.94 1799.41,1279.66 1801.93,1282.33 1804.44,1284.95 1806.96,1287.54 1809.47,1290.09 1811.99,1292.6 \n",
       "  1814.5,1295.06 1817.02,1297.49 1819.53,1299.88 1822.05,1302.23 1824.56,1304.54 1827.08,1306.81 1829.59,1309.04 1832.11,1311.24 1834.62,1313.4 1837.14,1315.52 \n",
       "  1839.66,1317.61 1842.17,1319.66 1844.69,1321.67 1847.2,1323.65 1849.72,1325.59 1852.23,1327.5 1854.75,1329.38 1857.26,1331.22 1859.78,1333.03 1862.29,1334.8 \n",
       "  1864.81,1336.54 1867.32,1338.25 1869.84,1339.93 1872.35,1341.58 1874.87,1343.19 1877.38,1344.78 1879.9,1346.33 1882.41,1347.86 1884.93,1349.35 1887.44,1350.82 \n",
       "  1889.96,1352.26 1892.47,1353.67 1894.99,1355.05 1897.5,1356.41 1900.02,1357.73 1902.54,1359.03 1905.05,1360.31 1907.57,1361.56 1910.08,1362.78 1912.6,1363.98 \n",
       "  1915.11,1365.15 1917.63,1366.3 1920.14,1367.42 1922.66,1368.53 1925.17,1369.6 1927.69,1370.66 1930.2,1371.69 1932.72,1372.7 1935.23,1373.69 1937.75,1374.66 \n",
       "  1940.26,1375.6 1942.78,1376.53 1945.29,1377.43 1947.81,1378.32 1950.32,1379.18 1952.84,1380.03 1955.35,1380.86 1957.87,1381.66 1960.38,1382.45 1962.9,1383.23 \n",
       "  1965.42,1383.98 1967.93,1384.72 1970.45,1385.44 1972.96,1386.14 1975.48,1386.83 1977.99,1387.5 1980.51,1388.15 1983.02,1388.79 1985.54,1389.41 1988.05,1390.02 \n",
       "  1990.57,1390.62 1993.08,1391.2 1995.6,1391.76 1998.11,1392.32 2000.63,1392.85 2003.14,1393.38 2005.66,1393.89 2008.17,1394.39 2010.69,1394.88 2013.2,1395.35 \n",
       "  2015.72,1395.82 2018.23,1396.27 2020.75,1396.71 2023.26,1397.14 2025.78,1397.56 2028.3,1397.96 2030.81,1398.36 2033.33,1398.75 2035.84,1399.12 2038.36,1399.49 \n",
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       "  2066.02,1402.93 2068.54,1403.2 2071.05,1403.45 2073.57,1403.7 2076.08,1403.95 2078.6,1404.18 2081.11,1404.41 2083.63,1404.64 2086.14,1404.85 2088.66,1405.07 \n",
       "  2091.18,1405.27 2093.69,1405.47 2096.21,1405.66 2098.72,1405.85 2101.24,1406.03 2103.75,1406.21 2106.27,1406.38 2108.78,1406.55 2111.3,1406.71 2113.81,1406.87 \n",
       "  2116.33,1407.02 2118.84,1407.17 2121.36,1407.32 2123.87,1407.46 2126.39,1407.59 2128.9,1407.72 2131.42,1407.85 2133.93,1407.97 2136.45,1408.09 2138.96,1408.21 \n",
       "  2141.48,1408.32 2143.99,1408.43 2146.51,1408.54 2149.02,1408.64 2151.54,1408.74 2154.06,1408.84 2156.57,1408.93 2159.09,1409.02 2161.6,1409.11 2164.12,1409.19 \n",
       "  2166.63,1409.28 2169.15,1409.35 2171.66,1409.43 2174.18,1409.51 2176.69,1409.58 2179.21,1409.65 2181.72,1409.72 2184.24,1409.78 2186.75,1409.85 2189.27,1409.91 \n",
       "  2191.78,1409.97 2194.3,1410.02 2196.81,1410.08 2199.33,1410.13 2201.84,1410.18 2204.36,1410.23 2206.87,1410.28 2209.39,1410.33 2211.9,1410.38 2214.42,1410.42 \n",
       "  2216.94,1410.46 2219.45,1410.5 2221.97,1410.54 2224.48,1410.58 2227,1410.62 2229.51,1410.65 2232.03,1410.69 2234.54,1410.72 2237.06,1410.75 2239.57,1410.78 \n",
       "  2242.09,1410.81 2244.6,1410.84 2247.12,1410.87 2249.63,1410.9 2252.15,1410.92 2254.66,1410.95 2257.18,1410.97 2259.69,1411 2262.21,1411.02 2264.72,1411.04 \n",
       "  2267.24,1411.06 2269.75,1411.08 2272.27,1411.1 2274.78,1411.12 2277.3,1411.14 2279.82,1411.15 2282.33,1411.17 2284.85,1411.19 2287.36,1411.2 2289.88,1411.22 \n",
       "  2292.39,1411.23 \n",
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       "  1638.44,1084.94 1640.95,1088.19 1643.47,1091.41 1645.98,1094.59 1648.5,1097.75 1651.02,1100.87 1653.53,1103.96 1656.05,1107.02 1658.56,1110.05 1661.08,1113.05 \n",
       "  1663.59,1116.03 1666.11,1118.97 1668.62,1121.88 1671.14,1124.76 1673.65,1127.61 1676.17,1130.44 1678.68,1133.24 1681.2,1136.01 1683.71,1138.75 1686.23,1141.46 \n",
       "  1688.74,1144.15 1691.26,1146.81 1693.77,1149.45 1696.29,1152.06 1698.8,1154.64 1701.32,1157.19 1703.83,1159.73 1706.35,1162.23 1708.86,1164.71 1711.38,1167.17 \n",
       "  1713.9,1169.6 1716.41,1172.01 1718.93,1174.39 1721.44,1176.75 1723.96,1179.09 1726.47,1181.4 1728.99,1183.69 1731.5,1185.96 1734.02,1188.21 1736.53,1190.43 \n",
       "  1739.05,1192.63 1741.56,1194.81 1744.08,1196.97 1746.59,1199.1 1749.11,1201.22 1751.62,1203.31 1754.14,1205.38 1756.65,1207.43 1759.17,1209.46 1761.68,1211.47 \n",
       "  1764.2,1213.47 1766.71,1215.44 1769.23,1217.39 1771.74,1219.32 1774.26,1221.23 1776.78,1223.13 1779.29,1225 1781.81,1226.86 1784.32,1228.7 1786.84,1230.52 \n",
       "  1789.35,1232.32 1791.87,1234.1 1794.38,1235.87 1796.9,1237.62 1799.41,1239.35 1801.93,1241.06 1804.44,1242.76 1806.96,1244.44 1809.47,1246.1 1811.99,1247.75 \n",
       "  1814.5,1249.38 1817.02,1250.99 1819.53,1252.59 1822.05,1254.17 1824.56,1255.74 1827.08,1257.29 1829.59,1258.83 1832.11,1260.35 1834.62,1261.85 1837.14,1263.34 \n",
       "  1839.66,1264.82 1842.17,1266.28 1844.69,1267.72 1847.2,1269.15 1849.72,1270.57 1852.23,1271.97 1854.75,1273.36 1857.26,1274.74 1859.78,1276.1 1862.29,1277.45 \n",
       "  1864.81,1278.78 1867.32,1280.1 1869.84,1281.41 1872.35,1282.71 1874.87,1283.99 1877.38,1285.26 1879.9,1286.52 1882.41,1287.76 1884.93,1288.99 1887.44,1290.21 \n",
       "  1889.96,1291.42 1892.47,1292.62 1894.99,1293.8 1897.5,1294.97 1900.02,1296.13 1902.54,1297.28 1905.05,1298.42 1907.57,1299.54 1910.08,1300.66 1912.6,1301.76 \n",
       "  1915.11,1302.86 1917.63,1303.94 1920.14,1305.01 1922.66,1306.07 1925.17,1307.12 1927.69,1308.16 1930.2,1309.19 1932.72,1310.21 1935.23,1311.22 1937.75,1312.21 \n",
       "  1940.26,1313.2 1942.78,1314.18 1945.29,1315.15 1947.81,1316.11 1950.32,1317.06 1952.84,1318 1955.35,1318.93 1957.87,1319.85 1960.38,1320.77 1962.9,1321.67 \n",
       "  1965.42,1322.57 1967.93,1323.45 1970.45,1324.33 1972.96,1325.2 1975.48,1326.06 1977.99,1326.91 1980.51,1327.75 1983.02,1328.58 1985.54,1329.41 1988.05,1330.23 \n",
       "  1990.57,1331.04 1993.08,1331.84 1995.6,1332.63 1998.11,1333.42 2000.63,1334.2 2003.14,1334.97 2005.66,1335.73 2008.17,1336.48 2010.69,1337.23 2013.2,1337.97 \n",
       "  2015.72,1338.7 2018.23,1339.43 2020.75,1340.15 2023.26,1340.86 2025.78,1341.56 2028.3,1342.26 2030.81,1342.95 2033.33,1343.63 2035.84,1344.31 2038.36,1344.98 \n",
       "  2040.87,1345.64 2043.39,1346.29 2045.9,1346.94 2048.42,1347.59 2050.93,1348.22 2053.45,1348.85 2055.96,1349.48 2058.48,1350.1 2060.99,1350.71 2063.51,1351.31 \n",
       "  2066.02,1351.91 2068.54,1352.51 2071.05,1353.1 2073.57,1353.68 2076.08,1354.25 2078.6,1354.82 2081.11,1355.39 2083.63,1355.95 2086.14,1356.5 2088.66,1357.05 \n",
       "  2091.18,1357.59 2093.69,1358.13 2096.21,1358.66 2098.72,1359.19 2101.24,1359.71 2103.75,1360.23 2106.27,1360.74 2108.78,1361.24 2111.3,1361.74 2113.81,1362.24 \n",
       "  2116.33,1362.73 2118.84,1363.22 2121.36,1363.7 2123.87,1364.17 2126.39,1364.65 2128.9,1365.11 2131.42,1365.58 2133.93,1366.03 2136.45,1366.49 2138.96,1366.94 \n",
       "  2141.48,1367.38 2143.99,1367.82 2146.51,1368.26 2149.02,1368.69 2151.54,1369.11 2154.06,1369.54 2156.57,1369.95 2159.09,1370.37 2161.6,1370.78 2164.12,1371.19 \n",
       "  2166.63,1371.59 2169.15,1371.99 2171.66,1372.38 2174.18,1372.77 2176.69,1373.16 2179.21,1373.54 2181.72,1373.92 2184.24,1374.29 2186.75,1374.66 2189.27,1375.03 \n",
       "  2191.78,1375.39 2194.3,1375.75 2196.81,1376.11 2199.33,1376.46 2201.84,1376.81 2204.36,1377.16 2206.87,1377.5 2209.39,1377.84 2211.9,1378.18 2214.42,1378.51 \n",
       "  2216.94,1378.84 2219.45,1379.16 2221.97,1379.49 2224.48,1379.81 2227,1380.12 2229.51,1380.44 2232.03,1380.74 2234.54,1381.05 2237.06,1381.36 2239.57,1381.66 \n",
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       "  2267.24,1384.77 2269.75,1385.04 2272.27,1385.31 2274.78,1385.57 2277.3,1385.83 2279.82,1386.08 2282.33,1386.34 2284.85,1386.59 2287.36,1386.84 2289.88,1387.08 \n",
       "  2292.39,1387.33 \n",
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      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_grid= -4:0.01:4\n",
    "\n",
    "p2 = plot(x_grid,pdf(Normal(),x_grid),label = \"Normal distribution\", \n",
    "    legend=:topleft, xlabel = L\"x\", ylabel=\"Density\",lw=2,legendfont=font(12))\n",
    "plot!(x_grid,pdf(Laplace(),x_grid),label = \"Laplace distribution\", lw=2)\n",
    "\n",
    "# plot(p1,p2,size=(1000,400),margin=10mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "savefig(\"~/Dropbox/MathEngDeepLearningBook/LaTeXBook/figures/chapter_2_figures/pdf_funs.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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